Chiral charge dynamics in Abelian gauge theories at finite temperature

Abstract

We study fermion number non-conservation (or chirality breaking) in Abelian gauge theories at finite temperature. We consider the presence of a chemical potential $\mu$ for the fermionic charge, and monitor its evolution with real-time classical lattice simulations. This method accounts for short-scale fluctuations not included in the usual effective magneto-hydrodynamics (MHD) treatment. We observe a self-similar decay of the chemical potential, accompanied by an inverse cascade process in the gauge field that leads to a production of long-range helical magnetic fields. We also study the chiral charge dynamics in the presence of an external magnetic field $B$, and extract its decay rate ${\Gamma }_5\equiv -\frac{d\log \mu }{dt}$. We provide in this way a new determination of the gauge coupling and magnetic field dependence of the chiral rate, which exhibits a best fit scaling as ${\Gamma }_5\propto e^{11/2}{B}^2$. We confirm numerically the fluctuation-dissipation relation between ${\Gamma }_5$ and ${\Gamma }_{\mathrm{diff}}$, the Chern-Simons diffusion rate, which was obtained in a previous study. Remarkably, even though we are outside the MHD range of validity, the dynamics observed are in qualitative agreement with MHD predictions. The magnitude of the chiral/diffusion rate is however a factor $\sim 10$ times larger than expected in MHD, signaling that we are in reality exploring a different regime accounting for short scale fluctuations. This discrepancy calls for a revision of the implications of fermion number and chirality non-conservation in finite temperature Abelian gauge theories, though not definite conclusion can be made at this point until hard-thermal-loops (HTL) are included in the lattice simulations.

Comments: 32 pages, 11 figures. V2: Improved introduction, added some discussions and references. Corrected typos. Corresponds to published version